Quasi-Newton particle Metropolis-HastingsE-mail address to corresponding author: [e-mail]. This work was supported by: Learning of complex dynamical systems (Contract num. 637-2014-466), Probabilistic modelling of dynamical systems (Contract num. 621-2013-5524) and CADICS, a Linnaeus Center, all funded by the Swedish Research Council

• Published in: IFAC-PapersOnLine 2015, Vol.48 (28), p.981-986
• Main Authors: Dahlin, Johan, Lindsten, Fredrik, B. Schön, Thomas
• Format: Article
• Language: English
• Subjects: approximate Bayesian computations; Bayesian parameter inference; particle Markov chain Monte Carlo; state space models; α-stable distributions
• ISSN: 2405-8963; 2405-8963
• DOI: 10.1016/j.ifacol.2015.12.258

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods.We exemplify this application and the benefits of the new proposal by modelling log-returns offuture contracts on coffee by a stochastic volatility model with α-stable observations.